Plates I: Deformation and Energy

This lecture covers the deformation of plates in pure bending, the total strain energy involving in-plane stretching and out-of-plane bending, and the phenomenon of wrinkling. The slides discuss the application of Kirchhoff's equations, the concept of curvature, and the assumptions made for slender plates. The lecture also delves into the constitutive law for plates, the consequences of certain assumptions, and the displacement field of the mid-plane. The discussion extends to the strain tensor, the stress tensor, and the energy of plate bending in one direction. Wrinkling and buckling phenomena are explored, along with the energy considerations and the implications of substrate stiffness on wrinkling. Various applications and case studies are presented, including the behavior of thin elastic membranes on different substrates and the transition from wrinkles to folds under compression.